EXACT MEASUREMENTS 

IN 

r EDUCATION 



JAMES LEROY STOCKTON. A. M. (Columbia) 

SUPERINTENDENT ELEMENTARY DEPARTMENT 
NORMAL SCHOOL, WINONA, MINN. 




CHICAGO NEW YORK 

ROW, PETERSON & COMPANY 



A 



EXACT MEASUREMENTS 

IN 

EDUCATION 



JAMES LEROY STOCKTON, A. M. (Columbia) 

SUPERINTENDENT ELEMENTARY DEPARTMENT 
KORMAL SCHOOL, WINONA, MINN. 




CHICAGO NEW YORK 

ROW, PETERSON & COMPANY 



xv"^^ 



v^^^ 



COPYBIGHT, 1915 
BY 

James LeRoy Stockton 



JAN 25 1915 

©CI.A392812 



EXACT MEASUREMENTS 

IN 

EDUCATION 

THESES 

I. Measurement in Education should have for 
its goal the computation of work and rate-of-work 
(power), in the sense in which these terms are 
used in Mechanics. 

II. Scales of force, space, and time, exist, or 
can be made, for school subjects; and the stand- 
ard units of these scales of force, and space, and 
time, should be combined into standard units of 
work and rate-of-work (power), such units 
directly corresponding to the foot-pound and the 
horse-power. (In this paper units are worked 
out for penmanship, and illustrated by experi- 
mental work involving certain applications of the 
Thorndike Scale.) 

III. Many units in many school subjects should 



4 EXACT MEASUREMENTS 

be supplemented by a single unit, making possible 
the computation of mental work and rate-of- 
mental-work (mental power) in all school sub- 
jects. The force involved in this computation is 
intelligence; the space is measured in elements of 
expression. (As there is no adequate scale of 
intelligence uncombined with any mechanical fac- 
tor, a theory of the necessary scale is ventured.) 

IV. In any case, to consider either force, space, 
or time, alone, or to combine them in an arbitrary 
manner, gives unreliable results. [This is shown, 
for computations in school subjects, by the pen- 
manship illustration. For computations of men- 
tal work, and mental power, experience with the 
Binet-Simon tests is cited in proof of the con- 
tention.] 



EXACT MEASUREMENTS IN EDUCATION 

I 

Most persons do not any longer question the 
possibility of measurement in Education, because 
it has become apparent that measurements always 
have been made, and are continuing to be made. 
When it is said that a piece of work is good, bad, 
or indifferent, a measuring scale of at least three 
steps is evidently being used. If papers are 
marked A, B, C, D, E, according to the judgment 
of the examiner, a scale of five steps is being used. 
This is clearly evident; measurement is a fact 
in all departments of Education whenever the 
value of the product is expressed. 

There are, however, many conscientious think- 
ers who still question the degree of exactness to 
which the measurement should be carried. The 
common rough measurements which are con- 
stantly used do not seem so objectionable as the 
more exact scientific measurements which are 
being proposed. It is feared that too much exact- 
ness will make Education formal or mechanical. 



6 EXACT MEASUREMENTS 

If this fear were justifiable it would furnish a 
very strong foundation for a stand against meas- 
urement, for modern Education cannot defend 
formalism. Fortunately, however, the difficulty 
can be met with the following statements : 

(1) Education, in so far as it can be measured, 
is a product, 

(2) Mechanical methods of measuring a prod- 
uct do not require mechanical methods of pro- 
ducing that product. Handwriting might be 
measured by the most mechanical means one could 
imagine, and yet have been produced by the freest, 
most spontaneous method that exists. The worst 
that can be said is that mechanical measurement 
may, in the careless and unthoughtful, tend to 
produce mechanical methods of production; but 
pre-supposing reasonable thoughtfulness in its 
use, nothing promises more for Education than 
does exact scientific measurement. 

In this work progress has been made through 
the establishment of relatively exact scales in 
certain school subjects ; but the progress has been 
slow, as it always is in a new field. Confusion, 
also, is beginning to result, because the plunge 
into this undiscovered country has naturally been 



IN EDUCATION J 

made with no very definite route marked out in 
advance, and with no very adequate conception 
of the extent of the territory to be explored. 
There is not much evidence that it is realized that 
the makin^^ of scales may be merely a scouting 
on the frontier — merely the beginnings of roads 
whose end lies in a more remote country. If 
this should prove to be true much wandering will 
be prevented if a return is made to the starting 
point, and an attempt made, in the light of all 
past experience, to map the whole route from 
the beginning to the end. Then if the map shows 
districts to be traversed in which as yet no road 
exists, the problem will at least be clear when 
these sections are reached. 

It is the purpose of this paper to suggest that 
an unexplored district does exist in the field of 
measurement in Education, and that the making 
of scales takes the investigator only part way on 
the road to the final goal. An attempt will be 
made to show that even with the scales now avail- 
able, or with other similar ones which may be 
made, still another step must be taken or Educa- 
tion remains in the same condition as was the 
science of Mechanics before the time of Watt. 



8 EXACT MEASUREMENTS 

Before Watt the scales of feet, pounds, and min- 
utes were in use, but there was no attempt to use 
them in a computation of work and rate-of-work 
by means of the composite units called the foot- 
pound and the horse-power. The formulation of 
these units opened a new realm in Mechanics. 
From now on this discussion will deal with the 
hypothesis that there is such a new realm in 
measurement in Education, and that all of our 
efforts in this field, including the making of scales, 
will gain in definiteness and worth through being 
directed toward this final goal — the computation 
of work and rate-of-work; work being used in its 
technical meaning for the science of Mechanics. 

Any hypothesis, in order to justify itself, must 
show wherein it meets conditions unmet before; 
it gains its adherents through its ability to clear 
up existing confusions, and to present worthy 
results. Therefore the problem squarely in view 
is (1) to show that there is confusion, (2) to show 
that this hypothesis clears up at least some of it, 
and (3) to show that the results from the applica- 
tion of the h3rpothesis are reasonable and valuable. 

There are at least three points where confusion 
exists. The first is clearly stated by Whipple, 



IN EDUCATION . 9 

** Manual of Mental and Physical Tests, '^ as fol- 
lows. ** The question arises: shall efficiency be 
measured in terms of quality, excellence, delicacy, 
or accuracy of work, or shall it be measured in 
terms of quantity, rate, or speed of work? For 
this question no general answer can be given.'* 
Certain expedients are then suggested, but no 
final and exact program is outlined. An attempt 
will be made to show that the hypothesis of work 
clears up the problem of the true relation between 
quantitative and qualitative scales, which is the 
real problem propounded in the foregoing quota- 
tion. Another source of confusion, distinct, but 
indirectly included by Whipple in the lines just 
quoted, lies in the treatment of the time element 
involved in testing. This, when considered at all, 
is ordinarily carried as a separate index; but in 
many cases there is a tendency to neglect it 
entirely, often with grave results, as happens 
when two schools are compared in handwriting, 
without any consideration of the time involved 
in the production of the specimens. The need 
for a separate index vanishes under the hypothe- 
sis of worJc, and time receives its legitimate and 
necessary emphasis. The third source of confu- 



XO EXACT MEASUREMENTS 

sion is in the conception of efficiency itself. This 
conception is vague and indefinite. Various defi- 
nitions are contending for recognition. All school 
measurement is supposed to be directed toward 
the determination of relative efficiency, and yet 
there is disagreement as to what constitutes true 
efficiency. There can be no such disagreement 
under the hypothesis of work. 

These claims for the hypothesis must now be 
more closely examined and tested. This task will 
be furthered by an analysis of mechanical work 
and rate-of-work. As already indicated, before 
the time of Watt the scales of feet, of pounds, and 
of minutes, were in use. It was therefore possible 
to know that a force of 5047.00 pounds was at 
work where it was found necessary to exert 
another force of 5047.00 pounds against it — as 
in lifting against the force of gravity. It was 
also easily seen that another valuable formulation 
could be made if distance were included. To say 
that one machine lifted a weight of 5047.00 pounds, 
and another a weight of 5556.00 pounds, led 
naturally to the idea that the second machine was 
the stronger; but as soon as the distance was 
taken into consideration a doubt was raised. If 



IN EDUCATION H 

the first machine raised 5047.00 pounds four feet, 
and the second machine raised its 5556.00 pounds 
four feet or more the doubt as to the greater 
strength of the second machine did not exist. 
But if the first machine raised 5047.00 pounds 
four feet and the second machine raised 5556.00 
pounds three feet, indefiniteness as to strength 
was apparent. It was possible to carry the two 
indexes in each case (5047.00 pounds lifted four 
feet, and 5556.00 pounds lifted three feet) and to 
get certain rather valuable results. One could 
say that he preferred the smaller amount lifted 
the greater distance, or the larger amount lifted 
the smaller distance; but the computation of work 
from these data made a single index possible, put 
definiteness into exact comparison of the two, and 
so opened the new realm as previously mentioned. 
Quoting from a modern text in physics: 
^^ When a body acted upon by a force moves in 
the direction in which the force is acting, work is 
said to be done. * * * The amount of work 
done is measured by the product of the force by 
the distance which the body moves along the line 
of the action of the force. Thus when a two 
pound weight is raised three feet, it moves a dis- 



12 EXACT MEASUREMENTS 

tance of three feet against a force of two pounds 
and therefore six foot-pounds of work is done 
against the force of attraction of the earth.''* 

Work, therefore, in Mechanics means force 
acting through space, and is computed by the 
formula W — F X S. Where work is to be con- 
sidered, force alone means nothing and space 
alone means nothing; but force acting through 
space means tvork, and a certain unit of force 
(the pound) acting through a certain unit of 
space (the foot) means a certain unit of work 
(the foot-pound). This unit of work may be 
briefly expressed as unit force acting through 
unit space. By means of this unit the two ma- 
chines above referred to may be definitely com- 
pared as to the work they do. One machine did 
work equal to 5047.00X4.00, or 20188.00 foot- 
pounds. The other did work equal to 5556.00 X 
3.00, or 16668.00 foot-pounds. The relative work- 
ing ability of the two machines is definitely ex- 
pressed by the ratio of 20188.00 to 16668.00. 

But there is still another element to be con- 
sidered; viz., that of time, The amount of work 



^Kimball — ' ' College Physics. ' ' 



IN EDUCATION 13 

is the same whether 5047.00 pounds be lifted 4.00 
feet in one minute or in one hour or in one year; 
but it is often important to know for various rea- 
sons, at what rate this work can be delivered. 
Hence another unit (a certain amount of work 
delivered in a certain time) becomes necessary. 
If a definite amount of work in a definite time is 
taken, it is not important just what the amount 
or the time may be, except for considerations of 
convenience. But if there is no unit agreed upon, 
two indexes must be carried as before, and com- 
parisons are again cumbersome. 20188.00 foot- 
pounds in five seconds, must perhaps be compared 
with 16668.00 foot-pounds in 51/2 seconds. In 
order to do this it must all be put upon the basis 
of amount delivered in one second by dividing 
the number of foot-pounds of work by the time. 
20188.00 foot-pounds divided by 5.00 = 4037.60 
foot-pounds per second; 16668.00 foot-pounds 
divided by 5.50 = 3030.54 foot-pounds per second. 
These can now be compared with each other. 

But it is still better to have a standard unit of 
accomplishment per second and compare all other 
accomplishments with the unit. Watt selected as 
the unit of rate-of-work the number of foot- 



14 EXACT MEASUREMENTS 

pounds per second accomplished by the average 
horse (550.00 foot-pounds per second). He could 
have used any other number, but this number 
proved convenient. Using it as a unit, it is seen 
that the machine which did 4037.00 foot-pounds 
per second was a 7.34 horse-power machine. The 
machine which did 3030.55 foot-pounds per second 
was a 5.51 horse-power machine. These two 
results admit of immediate and perfect compari- 
son, and the formulation of this method of com- 
puting rate-of-work (or power, as the physicist 
calls it) opened to Mechanics the second part of 
the new realm, as the computation of work itself 
opened the first part of that realm. 

In attempting to appropriate for Education 
this new field of work and rate-of-work (power) 
it is necessary to formulate units of work and 
rate-of-work (power) based upon either an anal- 
ogy to, or an identity with, force acting through 
space in time. Examination of the situation 
seems to show a real identity. That which is 
measured in Education is always some kind of 
expression through movement occurring in space, 
which movement is controlled (changed) either in 
direction or magnitude by some agent. The dif- 



IN EDUCATION 15 

ferences which we measure in handwriting are 
differences in direction and magnitude of motion, 
registered on paper in the form of letters. Even 
thought itself becomes manifest and can be meas- 
ured only in terms of expression, which expres- 
sion is in movement, resolved in the last analysis 
into changes in direction or magnitude. Now the 
only name the world has ever had for that which 
changes the motion of a body, either in direction 
or amount, is force. There seems to be no reason 
for calling the agent behind expression by any 
other name than force. It meets the definition of 
force, and is measured as all force must be; i. e. 
in terms of its products. There is therefore an 
identity between one element in units of work 
and rate-of-work (power) in Mechanics, and the 
same element in Education. (This affirmation of 
identity is meant to carry only so far as the 
assertion that the agent behind achievement in 
Education is a force. This force may differ from 
other forces, just as electrical force probably 
differs from gravitational force etc.) 

But all of the movements which are initiated 
and controlled by the force, take place in space 
and time. That is, the force acts through the 



16 EXACT MEASUREMENTS 

space in the production of the given movement in 
the given time. In handwriting when a word is 
written, the force (or control) acts through the 
space roughly measured by the linear arrange- 
ment of letters, this measurement being exactly 
parallel to the rough measurement of space by 
paces or other such linear units, used before the 
more accurate foot and inch where selected as 
units. The addition of the time element here as 
elsewhere, provides for the computation of rate- 
of-work, or power. This relation between force, 
space, and time is not an arbitrary but a natural 
and necessary relation. Physics demonstrated 
and adopted it; physics did not create it. The 
relation between the factors is a universal rela- 
tion which is found wherever the three factors 
are involved. 

Hence it seems inevitable to apply this prin- 
ciple in Education in a manner similar to its use 
in Mechanics.* 



*Reference is made earlier in this paper (page . . ) to 
certain attempts (see Whipple, Manual of Mental and 
Physical Tests) to correlate these factors. Reference 
should also be made to Brown's excellent article on 
Reading in the Elementary School Teacher for June, 



IN EDUCATION 17 

An attempt will now be made fully to illustrate 
and to apply the idea in the field of handwriting, 
since it is there that the most suitable scales nec- 
essary to the formation of the units are found. 
In handwriting there is motion under varying 
degrees of control. This control which alters the 
direction and magnitude of motion is a force. 
But the force here presents a complication of two 
factors; viz., conscious direction, which may be 
called intelligent force, or intelligence ; and habit, 
which is mechanical. It follows that the motion, 
then, is a resultant of the action of more than 
one force; but this does not alter anything in 
relation to the computations. A resultant of two 
or more forces is dealt with under the same laws 
as are simple forces. The one thing which must 
be remembered in this connection is that because 
the force, intelligence, is combined with a mechan- 
ical factor, the work computed cannot be called 
purely mental work but mere penmanship work. 



1914, and to others. In all cases, however, which have 
come under the observation of the writer of this article, 
arbitrary relations have been established among the fac- 
tors, and the necessary and permanent relation has been 
disregarded. 



18 EXACT MEASUREMENTS 

In the second part of this paper the discussion 
of the computation of purely mental work, where 
the force involved is intelligence alone, is con- 
sidered. 

Now in order to make the formulation of units 
possible, there must be a scale of the force and a 
scale of the space. Then the standard unit of the 
scale of force can be combined with the standard 
unit of the scale of space into the standard unit of 
penmanship work; and the standard unit of pen- 
manship work, complicated with the standard unit 
of a scale of time, can be the standard unit of rate- 
of -penmanship work, or penmanship power. But 
can the force involved in penmanship work be 
measured? Not directly, any more than the force 
of gravity can be measured directly. But the 
force of gravity is measured by its effects (ten- 
sion of a spring), and the force involved in pen- 
manship work can be measured by one of its 
effects; viz., the amount of quality exhibited by 
the handwriting produced. This amount of 
quality is, roughly at least, measured by the 
Thorndike handwriting scale, and the idea of 
such a scale is apparently sound and capable of 
refinement. Of this more will be said later. In 



IN EDUCATION 19 

the meantime this scale will be used as a means 
of continuing the illustration; and it should con- 
tinue to be used for purposes of school measure- 
ment until a better one takes its place, or until 
it is further made more nearly perfect. 

Let unit force (or control) be that control 
which produces penmanship which exhibits the 
amount of quality designated as No. 1 of the 
Thorndike scale. Let unit space be the space 
measured by one letter. Then if a person writes 
60.00 letters equal to No. 12.00 quality Thorndike 
scale, the work involved is force X space or 60.00 
X 12.00 or 720.00 units of work. These units 
correspond to foot-pounds and should be desig- 
nated by some name of similar significance. 

It is necessary at this point to guard against 
the idea that the plan as outlined above 
identifies force with quality of handwriting, and 
space with quantity of handwriting. The quality 
of the writing is not the force, but it is the 
measure of the force; the number of letters is 
not the space, but it is the measure of the space. 

Since quantity and quality are here mentioned, 
it seems best to discuss them further in order to 
show that the plan does give the combination of 



20 EXACT MEASUREMENTS 

quantitative and qualitative scales wliicli solves 
the vexed question (as claimed earlier in the 
paper). When it is said that a person does 60.00 
letters of No. 12.00 quality in a minute, and work 
is computed by finding the product of 60.00 and 
12.00 according to the formula W = F X S, 
viewed superficially it seems as if force were 
identified with quality and space with quantity, 
and that the two (quantity and quality) w^ere 
merely multiplied together as a solution of the 
quantity-quality difficulty. But force is not iden- 
tified with quality nor space with quantity; and 
when 60.00 is multiplied by 12.00 force is not 
being multiplied by space (as the formula F X S 
would seem to imply) but a measure of force is 
multiplied by a measure of space, as previously 
indicated. Neither when 60.00 is multiplied by 
12.00 is quality multiplied by quantity; but a 
quantity of quality, used as a measure of force, 
is multiplied by another quantity of quality, used 
as a measure of space. The Thorndike scale is 
a quantity-quality scale. No. 1 handwriting as 
measured by the scale exhibits a certain amount 
(quantity) of handwriting quality; No. 12.00 
handwriting, following the assumption of the 



IN EDUCATION 21 

author of the scale, exhibits an amount of hand- 
writing quality 12.00 times as great as that 
exhibited by No. 1 handwriting. That is to say 
that what we designate as No. 12.00 quality is not 
quality alone, but quantity of quality. It is the 
same with space. The unit of space in writing 
is the letter. This is rough, as has been admit- 
ted, but letters arranged in linear fashion meas- 
ure the space much as it might be measured by 
more or less irregular paces. 60.00 paces means 
60.00 movements of pace quality. Spaces and 
paces have many qualities all of which are not 
held in common, but one quality is common 
to both; viz., extension. Hence the extension 
involved in paces is often used to measure the 
extension of space. In like manner it is pro- 
posed to use the quality of extension involved in 
letters as a measure of the extension of space. 
One letter, therefore, is equal to a unitary 
amount (quantity) of the space quality known 
as extension. Therefore the multiplication of 
60.00 by 12.00 in the problem above cited, and in 
all similar problems, while it seems to be a mul- 
tiplication of quantity by quality, and actually 
settles our confusion as to the relation of these 



22 EXACT MEASUREMENTS 

scales, is really a multiplication of a quantity of 
quality by another quantity of quality ^ or in other 
words a multiplication of quantity by quantity. 
A summary of points thus far made follows: 
Exact measurement in Education is desirable 
and much has been done; but there is a realm 
into which it has not been extended; this is the 
realm of wo^'k. Computation of work requires 
the consideration of force acting through space. 
There must be a quantitative scale of some meas- 
ure of the force, made in definite standard units 
which can be counted, and the steps of the scale 
must bear a definite and known relation to one 
another. There must also be a definite scale of 
the space, meeting the same conditions as does 
the scale for the measurement of the force. Then 
the standard units of these scales must be com- 
bined into a composite unit of work, comparable 
to the foot-pound. So far it has been sho^oi how 
the conditions can be met for handwriting: the 
Thorndike scale is used as the measure of the 
force. No. 1 handwriting being the unit; letters 
are used to measure the space, one letter being 
the unit. Combining these standard units into 
a composite unit of work gives One Letter — 



IN EDUCATION 23 

No. 1.00 T scale as the result; the 60.00 letters 
No. 12.00 ^ scale equal 720.00 units of work 
(using the formula W = F X S). 

Now it becomes necessary to compute rate-of- 
work, and a unit must be found. When Watt 
wished to compute rate-of-work (power) he had 
to settle upon a representative number of foot- 
pounds per unit of time as a unit. So for hand- 
writing there must be selected a certain number 
of letters No. 1.00 T scale per unit of time. Any 
number would do, provided that it was definite 
and agreed upon, and used by every one. But 
for comparative purposes (in order that the unit 
may stand as a sort of goal of achievement) it 
is desirable that the number be put at some point 
near, probably slightly above, the average combi- 
nation of speed and control possible for the 
average seventh and eighth grade public school 
pupil. However, since all seventh and eighth 
grade public school pupils write above No. 1.00 
T scale handwriting, it is most feasible to get 
the average of both speed and control for such 
pupils, and then to reduce that number to No. 
1.00 quality. 

If these suggestions are carried out and the 



24 EXACT MEASUREMENTS 

riglit computations made, there is added to meas- 
urement in handwriting (and by the same meth- 
ods there could be added to the measurement of 
any other school subject) the realm of computa- 
tion of work and rate-of-work (power) which 
Watt added to Mechanics. The tendency in 
handwriting measurement has been to take the 
product of one school and measure by the Thorn- 
dike (or other) scale and get the average control. 
Then to take another school and do the same and 
compare the two results. This is exactly similar 
to that measurement in Mechanics which con- 
siders how much a machine can lift against the 
force of gravity but does not ask through what 
space the force acts, nor in what time the effort 
is performed. Some investigators have seen this 
difficulty and have set a time limit upon the 
making of the specimens and have counted the 
words or letters written in a certain time. But 
these results have been carried in a form not 
suitable for actual comparisons. It is much as 
if one tried to compare two machines by saying 
the one could lift ten pounds two feet in one 
second, and the other nine pounds two and one- 
half feet in one second, without trying to com- 



IN EDUCATION 25 

pute the work or the rate-of-work (powerj in- 
volved. To make units of work and rate-of-work 
(power) for penmanship (or other school sub- 
jects) solves the time problem mentioned in the 
early part of this paper, as it has been shown 
to have solved the quantity-quality problem. 

But in order to put the plan fully into opera- 
tion for handwriting, there is needed a knowl- 
edge of how many letters, and what quality of 
letters, the average seventh and eighth grade 
public school pupil writes per minute. To get 
at least preliminary light upon this matter, fifty 
such pupils were tested. Copying from the 
printed page under a set time limit was at first 
tried. Each pupil wrote three tests representing 
(1) his ordinary work, (2) his fastest work, and 
(3) his best work. These papers were scored 
for control by the Thorndike handwriting scale, 
and for space by the counting of the number of 
letters on the paper. Next an attempt was made 
to get truer data for writing per se, by eliminat- 
ing the perception element so common in the 
copying. This was done by asking the children 
to write memorized material. There were three 
^YQ minute tests as before; viz., (1) ordinary, 



26 EXACT MEASUREMENTS 

(2) rapid, (3) best. The tests were given to the 
children collectively and the papers scored as 
before for control and space. In all of the tests 
the same instructions were given to all of the 
children, the same part of the day was used, and 
in general, the usual precautions were taken to 
insure uniform validity in the results. 

Below is a table giving averages and the devia- 
tions from the average for both control and space 
in the full series of six tests. 
Abbreviations used: 

0. C. — Ordinary Copying 0. M. — Ordinary Memory 
H. C. — Hurried Copying H. M. — Hurried Memory 
B. C. — Best Copying B. M.— Best Memory 

Av. = average ; the tables are per minute of time. 

SPACE 



Av. 



Av. 



o.c. 


H.C. B.C. 


O.M. 


H.M. 


B.M. 


54.02 


77.48 49.60 

CONTROL 


75.07 


94.10 


60.07 


O.C. 


H.C. B.C. 


O.M. 


H.M. 


B.M. 


11.16 


10.44 11.40 


10.48 


9.66 


10.90 



IN EDUCATION 27 

AvEKAGE Deviations (from average) 





SPACE 




o.c. 


H.a B.C. 


O.M. H.M. B.M. 


12.56 


9.57 8.20 


9.79 12.30 9.48 



Av.... 



CONTROL 

O.C. H. C. B.C. O.M. H.M. B.M. 
Av 83 1.10 .84 1.20 1.40 .82 

This table does not involve enough cases to 
prove anything; but, in addition to presenting 
other interesting information, it does throw light 
upon the question as to what constitutes a reason- 
able unit of rate-of-work (power) in penmanship. 
No medians are given, but they correspond very 
closely to the various averages, and there seems 
to be little choice as to whether conclusions shall 
be drawn from the one or from the other. Since 
the results are suggestive only, it is simpler to 
deal with the averages only. The table of devia- 
tions will show that the deviation from the aver- 
age is but eight to twelve letters (or about two 
ordinary words) per minute. 

^\^ile fast handwriting and best handwriting 
present much material for comparison, it is, after 



28 EXACT MEASUREMENTS 

all, rather certain that ordinary writing is the 
best general measure. More than this, the 
tests marked '' ordinary memory '' are naturally 
selected, for '* ordinary copying '' was interfered 
with by the perception element. It will be seen 
that the space units under ordinary memory are 
75.07 and the control units 10.48. The ivoi^k is 
75.07 X 10.48 (F X S) or 786.73. Approximately 
this result has been selected as a possible unit of 
rate-of-work (780.00 letters of unit control in one 
minute). Certain undiscussed aspects of the 
problem make it seem that the factors here 
involved would represent a better standard to 
strive for if the relation were changed to 65.00 
and 12.00. This combination represents the same 
number of units of work (780.00) and will be 
dealt with in this paper tentatively as the stand- 
ard. Thorndike in his monograph on hand- 
writing suggests the same amount of work (60.00 
letters of 13.00 times unit control) as a limit 
beyond which it is useless to train children in 
this subject. 

The tentative units suggested for handwriting 
are therefore: 



IN EDUCATION 29 

Unit of work = One Letter — No. 1.00 T scale. 
Unit of rate-of-work (power) == 780.00 letters 
— No. 1.00 T scale, in one minute. 

If this represents a fair achievement in hand- 
writing, or if it does not and yet can be agreed 
upon as a measure, it will furnish a much more 
accurate and fair means of comparison than has 
heretofore been in use. 

The handwriting of pupil No. 1 scaled 12.00 
(Thorndike scale). The handwriting of pupil 
No. 5 scaled 10.00. Using the Thorndike scale 
as it is often used, this is as far as the matter 
would be carried and it would be said that pupil 
No. 1 was the better pupil in handwriting. What 
can rightly be said is that pupil No. 1 exhibited 
the most handwriting control. But it is impor- 
tant also (for complete comparison) to deal with 
other factors. First, throu^ what space was 
this average control sustained? Through 265.00 
letters for pupil No. 1, and through 387.00 letters 
for pupil No. 5. Now which is ** better'' — 
265.00 letters of No. 12.00 control or 387.00 letters 
of No. 10.00 control! There has been no way of 



30 EXACT MEASUEEMENTS 

telling at all accurately, and no system of com- 
putation will ever tell which is better. The ques- 
tion of best all depends upon the definition of 
best, upon the aim toward which the work is 
directed, and upon the degree to which the aim is 
accomplished. For certain purposes, 387.00 let- 
ters of No. 10.00 control may be much better than 
265.00 letters of No. 12.00 control (or vice versa). 
Control may for certain purposes be preferred 
to space, or excessively slow writing, for certain 
other purposes, may not be so good as more 
rapid work of less control. But though the 
knowledge of the aim may change the judgment 
as to which is best, it does not at all change the 
amount of work delivered. This amount of work 
delivered is a constant (for pupil No. 1, 265.00 X 
12.00 units of work) and to make use of it opens 
to Education one-half of the new realm of work 
added to Mechanics by Watt. 

Pupil No. 1 did 265.00 letters of No. 12.00 
control, or 3180.00 units of work. (A name must 
be coined for this unit.) 

Pupil No. 5 did 317.00 letters of No. 10.00 con- 
trol, or 3170.00 units of work. 

To have tried to compare these two items by 



IN EDUCATION 31 

carrying the two indexes would have been indefi- 
nite and burdensome; but to compare 3180.00 
with 3170.00 is simple and accurate. [This 
means accurate to the degree to which the scales 
involved are accurate, and though the scales are 
rough as yet, they are capable of refinement. A 
partial discussion of this matter follows later in 
regard to the Thorndike scale.] 

It is desirable also to add the time element and 
to know which of these pupils worked at the 
faster rate, for time is always an important 
factor in any task, although there are, of course, 
occasions when one is willing to sacrifice this 
element to other elements. Pupil No. 1 did 
3180,00 units of work in 5.00 minutes, or 636.00 
units per minute. Since 780.00 units per minute 
has been tentatively selected as a standard unit 
of rate-of-work, this pupil No. 1 exhibited less 
than one standard unit of rate-of-work (power) ; 
i. e. 636.00 divided by 780.00 = .81 units of rate- 
of-work (power). A name must also be coined 
for this unit. This name will correspond to the 
** horse-power " as used in Mechanics, as the 
name for the penmanship unit of work will corre- 
spond to the foot-pound. Pupil No. 2 did 3170.00 



32 EXACT MEASUREMENTS 

units of work in 5.00 minutes, or 634.00 units per 
minute. 634.00 divided by 780.00 = .81 units of 
rate-of-work (power). 

Here are two pupils who in work delivered 
(computed to two decimal places) are equal; but 
no such judgment could have been made from a 
mere examination of the data, or from the carry- 
ing of separate indexes. A definite unit of rate- 
of-work (power) based upon a unit of work 
makes this comparison possible. 

Even at the risk of being called to account for 
unnecessary repetition, it must again be said 
that there is no thought that these computations 
have proved what is the best condition. They 
have merely expressed accurately the facts of the 
condition. The question of best or worst is to 
be decided on the basis of the aims for the work. 
One may go intelligently about the task (on the 
basis of his aim) of producing any ratio between 
the factors of force-time-space that he may desire. 
Any adjustment of these factors may be sought, 
just as in the movement of physical weights a 
small force working through a long distance may 
be preferred, or a large force working through 
a short distance. The time element may also be 



IN EDUCATION 33 

long or short — all of these elements varying 
according to the aim. 

However, should there still be a desire to 
retain in these combination results, the evidence 
by means of which at any time the exact figures 
for control and space could be regained, it may 
be done by the following process, and at the same 
time a valuable element may be added to the 
final result. Pupil No. 1 was found to be worth 
.81 units of rate-of-work (power), because he 
wrote 265.00 letters of No. 12.00 times unit con- 
trol in 5.00 minutes, or 53.00 letters of No. 12.00 
times unit control in one minute. His space was 
therefore 53/65 of normal and his control 12/12 
of normal. These fractions may be observed, 
and on the basis of the aim for this work (which 
may require a preponderance of space or con- 
trol) judgment may be made as to whether or not 
the combination is a good one. To facilitate this 
judgTQent the answer may be written .81, (53/65 
X 12/12). But this notation will be all the more 
valuable if these fractions are reduced to deci- 
mals, since their relation will then be much 
plainer. Following out this suggestion for the 
students just compared, it is written that 



34 EXACT MEASUREMENT 

pupil No. 1 delivered .81 units, (.81 X 1.00) ; 
pupil No. 5 delivered .81 units, (.97 X 0.83). 

The same method of comparison may be used for 
two schools. Below is a table giving averages 
and deviations from the average, in space and in 
control, for fifty normal school girls, in six tests 
similar to those reported upon for grade chil- 
dren. Following the table is a comparison of 
certain records of the normal school girls, with 
corresponding records of the grade children. 
Abbreviations used: 

0. C. — Ordinary Copying 0. M.— Ordinary Memory 
H. C. — Hurried Copying H. M. — Hurried Memory 
B. C— Best Copying B. M.— Best Memory 

Av. = average; the tables are per minute of time. 



Av. 



Av, 





SPACE 






o.c. 


H.C. B.C. 


O.M. H.M. 


B.M. 


74.88 


99.66 73.56 

CONTROL 


91.96 111.00 


81.74 


O.C. 


H.C. B.C. 


O.M. H.M. 


B.M. 


11.50 


11.00 11.80 


11.56 10.30 


11.78 



IN ErUCATION 35 

Average Deviations (from average) 



Av.. 





SPACE 








o.c. 


H.C. B.C. 


O.M. 


H.M. 


B.M. 


11.52 


12.46 9.42 

CONTROL 


9.84 


12.18 


10.75 


O.C. 


H.C. B.C. 


O.M. 


H.M. 


B.M. 


.66 


.68 .56 


.67 


1.07 


.69 



Av.... 

To compare the records in ordinary copying 
the following computations are made: 

Normal girls space average 74.88 ; control aver- 
age 11.50. 74.88 X 11.50 = 861.12 ; 861.12 divided 
by 780.00 = 1.10, (74.88/65.00X11.50/12.00) or 
1.10, (1.15 X .95). 

Elementary school space average 54.02; con- 
trol average 11.16. 54.02 X 11.16 = 602.86; 
602.86 divided by 780.00 = .77, (54.02/65.00 X 
11.16/12.00, or .77, (.83 X .93). 

By merely looking at the tables it could be 
seen that at all points in both space and control, 
the normal school students were ahead of those 
in the elementary school. It would also be pos- 
sible to tell how much they were ahead in space 
and in control, each one being considered sepa- 



36 EXACT MEASUREMENTS 

rately; but without some such process as the one 
suggested it could never be told how much the 
normal school was ahead in the actual amount 
of work delivered. But having computed the 
amount delivered in each case, the comparison 
could be made. 

It is known also that more work was done than 
was delivered. There was loss, just as there is 
loss in the working of an engine where fric- 
tion and other causes subtract from the power 
actually delivered. No machine delivers as much 
work as it actually does, and the percentage 
delivered varies constantly from day to day and 
even from hour to hour or moment to moment. 
To say that a machine is ten horse-power, means 
that it averages ten horse-power, or that it is 
ten horse-power at the time that the measure- 
ment is made. A badly adjusted carburetor or 
an excess of friction at a given point may make 
a gas engine lose almost any per cent of its 
power, even to not being able to run at all. A 
horse grown nervous from misuse may ^* jump 
up and down " in one place and pull nothing. 
A child (metaphorically speaking) might do the 
same thing when nervous over being asked to 



IN EDUCATION 37 

do his best work, or when indifferent through 
lack of motive (as might be true of ordinary 
work). He does a large amount of work, per- 
haps, or possibly he does not. Theoretically he 
should put into his work his whole self and the 
same se^f each time, and deliver, without waste, 
an equal amount of work in a given time, even 
though the factors of force, space, and time 
varied in the different cases. Practically he does 
not put in each time his whole self or the same 
self, and, also, there are many other sources of 
loss, so that in given periods of five minutes, or 
other time space, the amount of work actually 
delivered varies. Data computed from table No. 
1 (using averages, but remembering that results 
would be similar for individuals) show that work 
delivered in ** ordinary memory '^ was 786.73 
units (75.07X10.48); in 'Miurried memory'' 
909.00 units (94.10 X 9.66) ; and in " best mem- 
ory " 654.76 (60.07 X 10.90). Under the three 
different sets of conditions three different 
amounts of work were delivered. This is exactly 
what should be expected because of the varying 
conditions under which the work was done. No 
one as yet can point with certainty to the proved 



38 EXACT MEASUREMENTS 

reasons for the actual relations between the dif- 
ferent products, but it is easy to advance entirely- 
reasonable explanations. Worry, perhaps, or a 
habitual slowness where best writing is attempted, 
would account for the small amount of work 
delivered in ** best memory.^' It is difficult and 
nerve trying to attempt to make one's hand- 
writing better than it usually is. The attempt 
cuts down the space and does not largely increase 
the control. The loss in work delivered is there- 
fore great. On the other hand, it is usually not 
nearly so difficult or disconcerting to increase 
speed beyond one's average. The attempt to do 
best work is a cause not only of very slow prog- 
ress while letters and words are being written, 
but also of much loss between the separate letters 
or words. The attempt to do fast writing is the 
cause of a great gain in space (not much waste 
between letters or words), and while the loss in 
quality (control) is considerable, it is still not 
sufficient to overcome the gain in space, and the 
work is correspondingly greater. Where quality 
is required speed drops 1/5 from ordinary, and 
where speed is required, quality drops less than 
1/8 (see table No. 1 — memory tests). This 



IN EDUCATION 39 

seems to mean that there is less total loss in 
hurried work than in best work, and would corre- 
spond with the results one would naturally expect 
from the fact that school children are in the 
habit of doing much hurried writing at certain 
times, while they have certainly less habit of 
doing best work and consequently the loss is 
greater when best work is insisted upon. 

The facts just brought out tend to justify the 
third claim for the hypothesis of work; viz., that 
it settles the question of a net index of efficiency 
and opens the way toward a study of waste in 
Education. Using efficiency as it is used in 
Mechanics, it is the ratio of. work delivered to 
work done. This ratio expressed as a fraction 
is the net index of efficiency. It is not now 
known how to determine w^ork actually done. In 
handwriting, for example, it is known only how 
to determine work delivered and this requires 
the use of the plan suggested in this paper. 
There are few^, however, who would doubt that 
work done can eventually be measured, and when 
it is measured, the net efficiency index will be 
assured, and the way will be opened for attack 
upon the problem of waste. 



40 EXACT MEASUREMENTS 

Returning, however, to the consideration of 
work delivered in handwriting, it is apparent 
that the validity of the results depends upon the 
validity of the Thorndike scale, and upon the 
reliability of judgments of handwriting, which 
judgments are based upon the scale. Just as no 
additional accuracy is secured by carrying to 
three decimal places results based upon data 
carried to two decimal places only, so the 
accuracy of computations based upon imperfect 
scales is really no greater than the accuracy of 
the scales themselves, and of the judgments based 
upon the scales. At present both of these items 
(the accuracy of the scale and the accuracy of 
the judgment based upon the scale) may be ques- 
tioned, and corresponding allowance must be 
made in placing any dependence upon computa- 
tions involving units derived from the scales. 
Yet, even with the necessary allowance, valuable 
use of the units may be made. Also, the rough- 
ness of the scales, and of judgments based upon 
them, can be overcome, for handwriting as a 
product can be scaled accurately as to excellence. 
But in order to do this, a sufficiently large 
number of representative specimens must be 



IN EDUCATION 41 

available. One of the main objections to the 
Thorndike scale made by writing supervisors is 
that the specimens used were not representative 
of public school writing — that the specimens 
were all largely poor, or at least indifferent, and 
that the really good qualities were not fairly 
represented. However this may be, it at least 
raises the question of what grade of handwriting 
may properly be expected of public school chil- 
dren, and how is the quality of handwriting to 
be judged, anyhow! Did Thorndike have repre- 
sentative specimens and how is one to tell what 
is representative? The judgment of quality and 
therefore of the scale, must be based upon the 
opinion of some one as to what is or is not excel- 
lent. No machine can ever set up standards of 
excellence. No machine can ever decide as to 
whether a vertical or a slant penmanship is bet- 
ter, or as to whether legibility is worth more 
than beauty etc., etc. ; but agreement can be made 
upon these points, and when this has been done, 
it is conceivable that a machine could be made 
to tell whether or not a given specimen is up 
to the standard. Neither is it imperative that 
large numbers of persons should be employed in 



42 EXACT MEASUREMENTS 

the setting up of the standards, except in the 
sense that large numbers must agree to the stand- 
ard as set up. That is to say, in this case 
as elsewhere, all could defer to a single authority, 
and agree to accept the grading of one expert, 
and to use his scale. It is better, probably, to 
get the judgment of many experts, as Thorndike 
did, and to agree to abide by the collective judg- 
ment. But the fundamental thing is the agree- 
ment, just as in any. discussion there must be an 
agreement upon a definition of terms, after which 
it is possible for the persons to understand each 
other and to talk definitely in the terms of the 
agreement. 

Whether or not the Thorndike scale is the best 
upon which to agree, the future will tell. So 
far as the report shows, only a very general basis 
of judgment was proposed to the judges, and it 
is probable that before there can be a final scale 
a more definite agreement must be reached as 
to what constitutes excellence in handwriting. Is 
it beauty, neatness, size, slant, or legibility (mere 
legibility as was assumed in the making of the 
Ayres scale) 1 There seems to be at present no 
general agreement upon these points ; but never- 



IN EDUCATION 43 

theless the scales can be used profitably, and an 
understanding maintained in their use as long 
as it is known what they actually represent, no 
matter whether or not there is a final agreement 
as to what they might represent. If the terms 
are defined,^ the discussion can proceed on the 
basis of the definition, and the only further 
progress consists in the elaboration of a defini- 
tion which all can more fully accept. But 
granted the definition; i. e. the scale, a mechan- 
ical method of judging a certain specimen by the 
scale may be looked forward to. In the analysis 
of handwriting for the detection of forgeries 
such a method as been worked out. Enough of 
mechanical analysis is made so that the real 
essence of the particular writing is plainly seen. 
Looking to other fields it is recalled that a 
mechanical analysis of a play decides how much 
of it Shakespeare really wrote. In a similar way 
the authorship of a picture may be determined. 
It is in this direction that the movement will be 
made to remove the personal factor in scoring 
by such scales as the Thorndike scale in hand- 
writing. In the meantime Education is far better 
off with the imperfect scales which it has (even 



44 EXACT MEASUREMENTS 

with imperfect use of them) than it was before 
it had them; but this advantage can be immeas- 
urably increased if these scales are at once made 
to yield real units of work and rate-of-work 
(power). 

With this outlook, there must be scales and 
units in other subjects than penmanship, and 
other units of work and rate-of-work (power). 
This means many scales and many units in many 
specific subjects. Some of these scales are 
already extant and the work in making others 
will be worth all that it costs, for when they are 
made and gradually refined, and when from them 
real units of work and rate-of-work (power) have 
been made, and used as a basis for comparison 
of individuals and of schools, the progress 
involved will be very great. 



IN EDUCATION 45 



n 

But the solution of the problem of school meas- 
urement should not be limited to the computation 
of many kinds of work, by many standards, in 
many school subjects. There is a need for a 
single measure, covering all subjects, which shall 
give a sort of summary of the abilities of an 
individual or of a group. This has been gen- 
erally and correctly expressed as a need for a 
measure of intelligence itself; but it is also more 
than that. It is a need for the computation of 
that which, for want of a better name, may be 
called mental work. As already stated in another 
part of the paper, purely mental work cannot be 
computed so long as the force involved is partly 
intelligent and partly mechanical, as it is in hand- 
writing. But mental work can be computed by 
the plan already outlined for penmanship work, 
if intelligence is a force, and if it can be dealt 
with apart from any mechanical factors. It is 
believed that this can be done. 

Intelligence is a force, which by acting through 



46 EXACT MEASUREMENTS 

a certain space, does work. Intelligence should 
not be regarded as merely analogous to force. 
It should be identified with force, since it meets 
the requirements of the definition of force. It 
is that which changes (controls) the motion of 
bodies; it is that ^* which makes it happen.'' 
Just as much is known about it (and no more), 
as is known about other forces. It would not be 
known to exist were it not seen revealing itself 
in action. A way is later suggested for freeing 
it from mechanical factors. 

But as already suggested, the need is not met 
by the use of a scale of intelligence (force) alone. 
The main use for such a scale is for purposes of 
comparison, and for such purposes there must be 
considered, also, the space through which a given 
measure of the force acts in a given time. To 
forget this is to violate the same principle which 
is violated when the penmanship of schools is 
compared by stating control (quantity of quality) 
alone, without asking through how much space 
(number of letters) the control acts in a given 
time. So while intelligence is to be dealt with 
as a force, it must also be dealt with as acting 
through space. But does it act through space? 



IN EDUCATION 47 

It is certain that in so far as the presence of 
intelligence can be proved, the proof results from 
the observation of some kind of expression or 
action through which intelligence reveals itself. 
Action takes place in space, and the space may 
always be measured in the elements of the action. 
In handwriting the elements used were letters. 
In the broader attempt to measure the space 
through which intelligence acts, the expression 
is found to be not only in written words (or let- 
ters), but also in vocal sounds or in gestures 
which involve the body in whole or in part. 
While these different types of expression present 
many difficulties when the attempt is made to 
count their elements as a measure of space, yet 
the difficulties do not seem insurmountable, at 
least for the purpose of a rough scale. 

The problem, therefore, which is clearly in 
view, is that of regarding intelligence as a force 
acting through space, of scaling the force and 
of scaling the space, and of combining the stand- 
ard units of these two scales into a stand- 
ard unit of mental work (thereby also making 
possible a unit of rate-of-work) (power). A ten- 
tative method of scaling the space has already 



48 EXACT MEASUREMENTS 

been suggested; but what can be done with 
regard to a scale of the force, intelligence? It 
has already been said that we do not know what 
intelligence is, but its existence is proved just in 
the same way that the existence of other forces is 
proved ; viz., by its etf ects. It is not known what 
gravitation is, but the falling of unsupported 
bodies is accepted as evidence of gravitation. A 
study of the literature of psychology will show 
that in like manner, adjustment to environment is 
generally accepted as an indication of intelligence. 
Intelligence is here conceived as the indefinable 
subjective force which, through all degrees of 
consciousness and intention, ** makes it happen.'* 
But from this point of view mere adjustment, 
cannot be taken as definite proof of intelligence, 
for there are recognized certain unintelligent 
adjustments, and certain others which may or 
may not be intelligent. The tropisms of Loeb 
and the ** pure instincts '* of other writers, are. 
unintelligent because they are described as utiliz-. 
ing a sort of hair-trigger mechanism which re- 
quires for. its release no impulse of any kind 
from within, but merely the appropriate external 
stimulus. Other reactions which once required 



IN EDUCATION 49 

intelligence, may through use, come to be per- 
formed sometimes with and sometimes (rela- 
tively at least) without that factor, and there is 
no way for the observer to make a distinction. 
In the case of the responses gained by use, it 
can be known that a past intelligence has been 
exercised, but not proved that a current, imme- 
diate intelligence is being exercised. Current, 
immediate intelligence can be proved in one way 
only. The proof lies not in the tropisms which 
give an invariable response to fixed conditions, 
nor yet in the reactions which have become 
mechanized to a greater or lesser degree, and so 
may or may not be at the moment intelligently 
directed; but it lies in consistent and effective 
reaction to variable conditions — to conditions 
tvliich are novel at the time at which the reaction 
occurs. Such reactions introduce a factor of 
selection, and where this factor is observed a 
subjective control, intelligence, is inferred. 

Hence if intelligence is to be graded it seems 
logical to make the grading in terms of this same 
principle of effective reaction to novel conditions. 
This can be done, for there are already recog- 
nized a number of very distinct ways by which 



50 EXACT MEASUREMENTS 

living creatures respond to novel conditions with 
varying degrees of success. One list quite com- 
monly accepted contains (1) trial and error, (2) 
imitation, (3) *^ free ideas.'' Some psychologists 
prefer to alter this list, using in the lower stages 
other terms, such as tropism, instinct, or circu- 
lar process, and discriminating in the ^^ free 
idea '' stage distinct divisions, such as sugges- 
tion, dictation, association, and thought. There 
is probably no universally accepted list ; but since 
some definite list could certainly be agreed upon 
when the need for such agreement becomes evi- 
dent, any list may be taken for purposes of illus- 
tration. If such a list included (for example) 
(1) trial and error, (2) imitation, (3) suggestion, 
(4) association, (5) thought, then these would he 
the five grades in a scale of intelligence. 

But these grades must not be known, merely. 
They must be known in series, one higher in a 
scale than is another. And not only that, but the 
numerical relation between the grades must be 
known in order that any one of them may be 
expressed in terms of any other. In a general 
way it is accepted that imitation is higher (in a 
scale of intelligence) than is trial and error, and 



IN EDUCATION 51 

thought higher than either imitation or trial and 
error. That creature which can respond by trial 
and error only, would probably be least success- 
ful in meeting novel conditions, and therefore 
called least intelligent. That creature which 
could respond by imitation or by thought, would 
be more successful and would therefore be said 
to possess a higher grade of intelligence. But in 
relation to the principle of response to novel con- 
ditions, the order in which these types of 
response stand can be definitely determined; and 
not only the order, but also the mathematical 
relation between them. Through reasonable pa- 
tience in experimentation, the average percentage 
of success (per thousand or other large number 
of cases), occurring for each one of the types can 
be determined. The relation between successive 
percentages will he the relation between the steps 
of the scale. Tropism or some other method 
agreed upon as one which brings no success will 
be the zero. 

Preliminary work on such a scale is now being 
done by the writer, and if the results are suffi- 
ciently promising they will later be offered for 
criticism, and the aid of educational experts 



52 EXACT MEASUREMENTS 

sought in their revision. When there is such a 
scale of force and also a scale of space (which 
is likewise being worked upon), unit force and 
unit space can be combined into a composite 
quantity-quality unit of mental work. When this 
unit is complicated with unit time it will furnish 
a unit of rate-of -mental-work (mental power), 
which unit will be a fair one to use in compari- 
sons of individuals, of schools, or any other 
groups, because all factors will have been con- 
sidered. In connection with the unit there will 
be needed a series of tests, by the use of which 
data may be obtained for computations in terms 
of the units. This series of tests (largely similar, 
probably, to those by which the scale must be 
established) will, if successful, be such as to make 
it possible for subjects of all ages to be tested 
for the various grades of intelligence, and for 
the space through which the intelligence can act 
in a certain time. From these data the number 
of units of mental work can be computed. A 
purely arbitrary illustration is as follows : 

An intelligence of grade 6.00 acts through a 
space of grade 50.00 in one minute. 6.00 X 50.00 
(F X S) =300.00 units of mental work per min- 



IN EDUCATION 63 

ute. Suppose the standard (arbitrarily placed or 
found by experiment — see penmanship illustra- 
tion) to be 275.00 units per minute. 300.00 di- 
vided by 275.00 = 1.09 units of rate-of-mental- 
work (the rating of this imaginary individual at 
that time). 

It should be noted here that an increase or 
decrease in mental work does not necessarily 
mean an increase or decrease in the one factor, 
intelligence. The change may be in either of the 
other factors, the space or the time. The weight 
of this fact will be evident in what follows con- 
cerning the Binet-Simon tests of intelligence. 

No such discussion as this would be complete 
without a consideration of the Binet-Simon tests 
(the most popular of all the tests already avail- 
able which make any attempt to scale the force 
involved in a computation of mental work). 
These tests have given, and are continuing to 
give, very valuable service; but even their most 
enthusiastic advocates do not claim them to be 
tests of immediate (current) intelligence alone. 
Probably the most that can be said is that they 
are tests of a combination of immediate and past 
intelligence and of inherited mechanism. They 



54 EXACT MEASUREMENTS 

are tests of what a subject can do, as a result of 
his total equipment and experience. The intel- 
ligence which enabled him to meet novel condi- 
tions and to adjust himself to them, may or may 
not be present, for many of the tests do not call 
for a meeting of novel conditions at the time of 
the test, but for a repetition of acts the capability 
for doing which may have demanded a meeting 
of novel conditions in the past. This is one lim- 
itation upon the use of these tests for the pur- 
pose of obtaining data to be used in the computa- 
tion of mental work, for the computing of the 
mental work accomplished in any unit of time 
requires that the force involved in the computa- 
tion shall be immediate intelligence (adjustment 
to novel conditions at that time). 

It is also noted that the steps in the Binet- 
Simon scale are expressed in years, and it hardly 
seems possible that the mathematical relation 
between the accomplishment of the various years 
can ever be known accurately enough (even by 
the law of averages). Mental development does 
not seem readily measurable in years of life as a 
standard. It is at least unproved (and probably 
unclaimed) that the scale as it stands presents 



IN EDUCATION 55 

any way by which one grade couid be expressed 
in terms of any other grade. But if an expres- 
sion in equivalents could be approximated, and 
if the fact that immediate intelligence is not set 
squarely by itself could be temporarily over- 
looked, the scale would then be useable for at 
least rough computations ; but even then it would 
not be fair to test subjects and to use the data 
for comx)arison unless allowance were made for 
the error resulting from a failure to consider the 
space through which the force acts in a given 
time. As the tests now stand, this question is 
not raised except in a few specific instances. The 
examiner waits for the dull child, encourages or 
possibly forces him, as the case seems to require, 
in order to get his maximum effort without 
regard to time. Then he is given a certain 
** mental age '' because he passes a certain num- 
ber of points. If, now, a bright child be taken — 
one younger chronologically but quicker and more 
alive in every way — and if, in half of the time, 
results are easily obtained which indicate the 
same mental age, this procedure does not show 
that the two children belong together. Children 
belong together who are equal or approximately 



56 EXACT MEASUREMENTS 

equal in ability to do mental ivork. The real test 
must regard the space, and the time, and the 
force, and make work and rate-of-work (power) 
the basis for comparison. Then it will be found 
that two children such as those cited are far 
apart. It is found that children tested by the 
Binet-Simon tests, assigned the same mental age 
(below chronological age) and put in classes of 
normal children of the given mental age, are 
unable to do the work. Also, children found to 
be below normal age and segregated in special 
classes of supposed approximate ages are found 
not to work well together after a time. They 
are like swimmers who go at various rates and 
who constantly draw away from each other. 
These are the natural conditions which should 
he expected under a system of partial testing. 
The recognition of the fact that they work out 
as they do, throws weight in favor of the conten- 
tion that timCy force, and space should all be con- 
sidered, and that the computation of work and 
rate-of-work (power) is the ultimate goal of 
school measurement. 

[In this paper the units used have been pat- 
terned upon what the physicist calls his arbitrary 



IN EDUCATION 57 

units, sucli as those based upon gravitation. The 
physicist also uses other units called * * absolute ' * 
units, such as those based upon acceleration. 
Some of the phenomena of mental activity; e. g. 
the ** warming up '^ process, "Weber's law, and 
the fact that one probably accomplishes more per 
minute in the last minutes of a test than in the 
first — at least raise the question as to whether 
absolute units, based upon acceleration may not 
in the future find a place in the computation of 
mental work.] 



Credit is due to J. S. Gaylord, Phychology, Winona 
Normal School, and to W. H. Munson, Physics, Winona 
Normal School, for definite constructive criticism of this, 
paper. 



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The book gives a true portrayal of existing rural conditions ; 
presents a definite, constructive program for improvement ; and 
strikes a clear note of inspiration for organized endeavor. 

Principles of Teaching 

N. A. Harvey, 423 pp $1.25 

The aim has been to make a thoroughly practical book for 
all teachers. Almost every difficult problem the teacher has to 
face is discussed in an interesting, helpful way. Especially val- 
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of Play, Interest, Analysis of the Study Process, and Motives 
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Methods of Teaching 

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most stimulating and informing book, especially designed for 
use as a text in Normal and Training schools. 

The Personality of the Teacher 

Charles McKenny, 192 pp $1.00 

It is generally conceded that the prime factor in making a 
school is the personality of the teacher. The author shows 
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how to develop those qualities. The book cannot fail to prove 
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How to Teach Arithmetic 

J. C. Brown and L. D. Coffman, 384 pp $1.25 ^ 

The aim has been to present in a clear and definite way the 
principles and devices with which efficient teachers of Arith- 
metic should be familiar. 

The selection and arrangement of the material shows sound 
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The Educational Meaning of Manual 
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By R. K. ROW 
Cloth, 250 pages Price, $1.25 

The aim of the author is to present an or- 
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First: Defines the problem of the book. 

Second : Throws into perspective the history of the develop- 
ment of manual training as a factor in education. 

Third: Analyzes and explains the primary impulses and 
interests in manual activities. 

Fourth: Shows the relation of manual activities to sense 
training, motor control and neuro-muscular development. 

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Sixth: Shows to whom such training is of most value, out* 
lines a general method of teaching, and gives suggestions 
for a course of study. 

SOME ESTIMATES 

The most complete and intelligent thesis thus far published on the 
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Mr. Row never forgets the claims of education in vocation. His study 
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Mr. Row's discussion of intellectual, aesthetic, ethical, economic, and 
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r 



SCHOOL MANAGEMENT 

By ALBERT SALISBURY, Ph. D. 

President of the Whitewater State Normal School, author of 
"The Theory of Teaching," etc. 

Cloth, l2mo., 196 pages, $1.00 

This book represents the fruits of a lifetime spent in the schools 
and in the training of teachers. School conditions have changed 
greatly in recent years, and books on school economy which were 
excellent a few years ago are now antiquated. Much more is 
demanded of the teacher than formerly. He has, in fact, become 
an official of the state, with larger functions and a greater need 
for intelligence concerning those functions than the old-time 
pedagog. 

While endeavoring to recognize this newer conception of the 
teacher's office, and the greater burden which it imposes, it has 
been the desire of the author to make a small book rather than a 
bulky one, excluding padding and time-honored common>place. 
The book is intended to serve the needs of young teachers and 
those in preparation for the work, and clearness has been aimed 
at rather than profundity. 

Testimonials 

Frank A. Weld, Pres. State Normal School, Moorhead, Minnesota 

"1 have been reading Salisbury's 'School Management' with great interest. 
It is a stimulating book and should find its way into many Normal schools." 

Dr. A. E. Winship, Boston, Mass. 

"1 have spent more time on 'School Management' than I intended, because 
I have enjoyed it more than 1 expected to. It is in the fullest sense a notable 
book. It gives what is needed in the least space, in the best spirit, and in a 
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Charles A. Wagner, Dept. of Methods, S. N. S., West Chester, Pa. 

"1 have thoroughly enjoyed the sane views, the practical suggestions, and 
the vigorous treatment and language of Dr. Salisbury's 'School Management.' 
The book includes all the necessary new features, and omits quite as wisely as 
it includes. It is right in size, covers the necessary ground, and occupies safe 
and sane positions." 

Wisconsin Journal of Education, Madison, Wisconsin. 

"A long life in the schoolroom as a trainer of teachers and a man who has 
kept pace with educational progress. President SzJisbury has written a practical 
book with little theory and every paragraph driving home principles for the safe 
guidance of teachers. His vigorous style, his coming-to-the-point-quick man- 
ner of writing makes 'School Management' a volume full of nrieat and a most 
valuable addition to the present literature on this important subject." 

Sent postpaid to any address on receipt of price. 

LihtraJ discount to cJassts. 

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CHICAGO, ILLINOIS 



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